[petsc-dev] Discussion about time-dependent optimization moved from PR

[Stefano Zampini]

>
>> Point-form functionals (i.e., objective functions that are not integrated
>> over time, but just sampled at a given time) drive the initialization of
>> the adjoint variables, and they are not supported explicitly in Hong's
>> code. S: TSSetObjective()
>>
>
> Should these just be handled by a particular quadrature in the cost
> integral, and by this I mean functionals are specified by quadratures.
>

Yes, they are evaluated separately in the forward run, see

https://bitbucket.org/petsc/petsc/src/c2e9112e7fdfd89985f9ffc4d68b0d46cf7cad52/src/ts/interface/tspdeconstrainedutils.c?at=stefano_zampini%2Ffeature-continuousadjoint&fileviewer=file-view-default#tspdeconstrainedutils.c-420
https://bitbucket.org/petsc/petsc/src/c2e9112e7fdfd89985f9ffc4d68b0d46cf7cad52/src/ts/interface/tspdeconstrainedutils.c?at=stefano_zampini%2Ffeature-continuousadjoint&fileviewer=file-view-default#tspdeconstrainedutils.c-486
https://bitbucket.org/petsc/petsc/src/c2e9112e7fdfd89985f9ffc4d68b0d46cf7cad52/src/ts/interface/tspdeconstrainedutils.c?at=stefano_zampini%2Ffeature-continuousadjoint&fileviewer=file-view-default#tspdeconstrainedutils.c-539
https://bitbucket.org/petsc/petsc/src/c2e9112e7fdfd89985f9ffc4d68b0d46cf7cad52/src/ts/interface/tspdeconstrainedutils.c?at=stefano_zampini%2Ffeature-continuousadjoint&fileviewer=file-view-default#tspdeconstrainedutils.c-549

but their gradient wrt the state variables (for first-order adjoints)
dictates the initialization of the adjoint variables. More complicated
formulas for semi-explicit index-1 DAEs and second order adjoints (needed
by the Hessian matvec)

https://bitbucket.org/petsc/petsc/src/c2e9112e7fdfd89985f9ffc4d68b0d46cf7cad52/src/ts/interface/tsadjointts.c?at=stefano_zampini%2Ffeature-continuousadjoint&fileviewer=file-view-default#tsadjointts.c-700
https://bitbucket.org/petsc/petsc/src/c2e9112e7fdfd89985f9ffc4d68b0d46cf7cad52/src/ts/interface/tsadjointts.c?at=stefano_zampini%2Ffeature-continuousadjoint&fileviewer=file-view-default#tsadjointts.c-376



>
> For people like me who do not have all the terminology down, is the
> Tangent Linear Model (TLM) just the forward sensitivities?
>

Yes. See the man page for TLMTS for the Tangent linear model ODE.
https://bitbucket.org/petsc/petsc/src/c2e9112e7fdfd89985f9ffc4d68b0d46cf7cad52/src/ts/interface/tstlmts.c?at=stefano_zampini%2Ffeature-continuousadjoint&fileviewer=file-view-default#tstlmts.c-403


>
>>
>> 2017-10-15 18:14 GMT+03:00 Matthew Knepley <knepley at gmail.com>:
>>
>>> Someone had to do it.
>>>
>>> I will not try to frame the entire discussion. Barry has already thrown
>>> down the "show me your interface" gauntlet. However, I want to emphasize
>>> one point that may have been lost in the prior discussion. Every example I
>>> have looked at so far is focused on the reduced space formulation of the
>>> optimization problem. However, I am interested in the full space
>>> formulation so that I can do multigrid on the entire optimal control
>>> problem. This is not a new idea, in particular Borzi does this in SIAM
>>> Review in 2009. I think we have a tremendous opportunity here since other
>>> codes cannot do this, it has the potential (I think) for much better
>>> globalization, and perhaps can be faster.
>>>
>>> So, when we come up with interface proposals, I think we should keep a
>>> full space solution method in mind.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>> https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
>>>
>>
>>
>>
>> --
>> Stefano
>>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
>



-- 
Stefano
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